With an x-ray computed tomography method the object for which a projection dataset is to be acquired is generally exposed to x-ray radiation from a number of projection directions. An image dataset is then reconstructed from this projection dataset. This is generally done using a back projection method, in which in most instances the projection data acquired from the scanner of the x-ray computed tomography apparatus is preprocessed. A so-called rebinning step is then performed, in which the data generated with the beam propagated in the manner of a fan from the source is rearranged so that it is present in such a form as if the detector were struck by an x-ray beam wave front running in a parallel manner to the detector. The data that has been rearranged and filtered in this manner is then used for a back projection onto the individual image points within the volume of interest.
The standard method generally used here is a so-called filtered back projection method FBP. With this method the rebinned data is generally first transformed into the frequency range, where filtering takes place by multiplication using a convolution kernel. The filtered data is then back transformed and the back projection takes place with the filtered data. The selection of the convolution kernel allows the desired image characteristic, in particular the image sharpness and noise, to be influenced.
However such simple back projection methods have the disadvantage that the image sharpness is always linked to image noise. The greater the sharpness achieved, the greater the image noise and vice versa. Therefore iterative reconstruction methods have recently been developed, with which such limitations can be eliminated to some degree.
With such an iterative reconstruction method a reconstruction of initial image data from the measured projection data takes place first. A convolution back projection method for example can be used for this purpose. From this initial image data a “projector” (projection operator), which should map the measuring system mathematically as closely as possible, is then used to generate synthetic projection data. The difference in respect of the measurement signals is then back projected, thereby reconstructing a residue image, which can be used to update the initial image. The updated image data can in turn be used to generate new synthetic projection data in a next iteration step with the aid of the projection operator, to form the difference in respect of the measurement signals from this again and to calculate a new residue image, which can in turn be used to improve the image data of the current iteration stage.
Such a method allows image data to be reconstructed, which has relatively good image sharpness but still a low level of image noise. Such raw data-based or projection data-based iteration methods have the disadvantage of being very computation-intensive due to the necessary repeated virtual projections from the image data space into the projection data space and back projections from the projection data space into the image data space and therefore require extremely high-performance hardware.